Replotting data from a linear scale onto a logarithmic scale in order to test the data for exponential dependence has always been time consuming and often tedious. A need exists for display systems which can optically convert a linear representation to a logarithmic one.
This conversion is also needed for more sophisticated technology. With the advent of coherent optical correlation technology, character recognition (for reading machines) and terrain pattern recognition (for aerial reconnaissance, etc.) programs having received great emphasis in optical data processing. By means of lasers, halographic quality lenses and the fabrication of matched filters in the so-called Fourier Transform plane, certain patterns hidden among a confusion of shapes or background noise can be "recognized." This recognition consists of a strong optical signal in an output plane which contains the cross-correlation between the input image and matched filter. The location of this strong optical signal in the output plane is indicative of the location of the recognizable pattern in the input image. This recognition ability persists despite variation in image intensity, certain obscurations, and translation of the input image. However, if there is a magnification or scaling factor change between the input image and that which contained the reference pattern from which the matched filter was made, no strong, localized optical signal will result in the output plane. In other words, image recognition cannot take place after pattern magnification. This makes it impossible for coherent optical correlation systems to rapidly indicate recognizable content in an aerial reconnaissance photo unless the altitude (or, at any rate, the scaling of photo content) is identical for reference photos (from which matched fibers are made) and the photos to be examined.
The log-log scale refractor of the present invention is, in part, designed to solve the aforementioned problem of replotting data for which a logarithmic rendition is desired. This may be done quite simply by photographing the linear plot with polaroid transparency film, placing the transparency in a well-collimated light beam, allowing the modulated beam to pass through the log-scale lens (or simply log-scale lens, if desired), and viewing the result in a screen appropriately placed.
The log-log scale refractor is also disposed to eliminate the restriction that scaling factor (or magnification) be the same for reference and examined patterns in order to obtain "recognition" in coherent optical correlation systems. Such is possible with the log-log scale refractor. Provided the image content at the zero coordinate of the log-log scale refractor plane is the same for both reference pattern and examined pattern, a magnification of the examined pattern simply converts to translation of the log-log scale image. The optical correlation is fully capable of pattern recognition when mere translation is involved. The key to making this possible is adapting the system to recognize the log-log scale rendition of patterns, rather than linear scale renditions.